Is that a third party tool that you are using (separate from host a and b)? Also do you have fluctuations like that at other points in the year? If not, then it might be a good idea to have your host check the logs to see if visitors are receiving errors or if security is blocking some traffic. Conversely, if your previous host had a high amount of bad traffic making it to your site, then that might show up in your graph.
If you look at the graph the traffic pattern is very close for the two months. Look around 8th November traffic is down and December traffic is up. Looking at the end of the month it is almost dead even. Traffic patterns will never be the same month to month. If you had no traffic I'd be worried.
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